Absolutely closed nil-2 groups

Details Absolutely closed nil-2 groups Absolutely closed nil-2 groups

1998-03-11

arxiv.org/abs/math/9803042v4

Algebra Universalis 42 (1-2) pp. 61-77 (1999)

Mathematics

Group Theory

21 pages plain TeX. Final version, with full classification

Scientific paper

Using the description of dominions in the variety of nilpotent groups of
class at most two, we give a characterization of which groups are absolutely
closed in this variety. We use the general result to derive an easier
characterization for some subclasses; e.g. an abelian group $G$ is absolutely
closed in ${\cal N}_2$ if and only if $G/pG$ is cyclic for every prime $p$.

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